GMAT algebra strategies

GMAT algebra tests your ability to translate a word problem into an equation before you solve anything. These strategies cover setting up equations from scratch, factoring quadratics efficiently, the wrong-variable trap the answer choices are built around, and a worked example you can follow step by step.

The core principle

Set up the equation from the word problem before you solve it. Most algebra errors happen in the translation, not in the solving. If a problem says a number is 5 less than twice another number, the equation is $x = 2y - 5$ before you touch a single operation. Define your variables, write the equation, then solve. A clean setup makes the algebra trivial and keeps you from back-solving the wrong quantity.

Factoring the difference of squares

The GMAT rewards fast factoring. The pattern that appears most often is the difference of squares: $a^2 - b^2 = (a + b)(a - b)$ . When you see $49 - 25$ , do not multiply. Recognize it as $7^2 - 5^2 = (7 + 5)(7 - 5) = 12 \times 2 = 24$ . The same pattern solves $x^2 - 16 = 0$ instantly: $(x + 4)(x - 4) = 0$ , so $x = 4$ or $x = -4$ . Spotting the pattern is faster than the quadratic formula every time.

The most common trap

Solving for the wrong variable

The question asks for John's age in 5 years, but you defined $x$ as John's current age and solved for $x$. You picked the answer that matches $x$, but the question wanted $x + 5$. The answer choices include both $x$ and $x + 5$ because the test writers know this mistake. Always underline what the question asks for before you solve, and verify your final value answers that question, not the variable you defined.

Step-by-step strategy

When to use: any word problem that describes a relationship between quantities, or any equation the GMAT asks you to solve.

1Define variables for every unknown, and write down what the question asks for separately.
2Translate the words into equations, one sentence at a time.
3Solve using substitution, elimination, or factoring. Look for the difference of squares before reaching for the quadratic formula.
4Verify the answer matches what the question asked for, not the variable you defined.

When not to use: when the problem is pure arithmetic or when you can backsolve from the answer choices faster than setting up.

Worked example

The sum of two numbers is 40. If 3 times the smaller number is 10 more than twice the larger number, what is the larger number? Step 1: Define variables. Let $s$ be the smaller number and $l$ be the larger number. The question asks for $l$ . Step 2: Translate. The first sentence gives $s + l = 40$ . The second gives $3s = 2l + 10$ . Step 3: Solve. From the first equation, $s = 40 - l$ . Substitute into the second: $3(40 - l) = 2l + 10$ . Expand: $120 - 3l = 2l + 10$ . Rearrange: $110 = 5l$ . So $l = 22$ . Step 4: Verify. The larger number is 22, the smaller is 18. Three times 18 is 54. Twice 22 plus 10 is 54. The check passes. The answer is 22.

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Word problems strategies

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